Character sheaves on disconnected groups, IX
We associate a two-sided cell to any (parabolic) character sheaf. We study the interaction of the duality operator for character sheaves and the operation of "twisted induction".
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arXiv subjects
G. Lusztig
Publications and source records attributed to G. Lusztig.
Character sheaves on disconnected groups, VIII
In this paper we continue the study of character sheaves on a reductive group G. To each subset of the set of simple reflections in the Weyl group we associate an algebra of the same kind as an Iwahori-Hecke algebra with unequal parameters in terms of parabolic character sheaves. We also prove a Mackey type formula for character sheaves. We define a duality operation for character sheaves. We also prove a quasi-rationality property for character sheaves.
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Unipotent elements in small characteristic
We make a study of unipotent elements in a connected reductive group over an algebraically closed field with emphasis on the case where the characteristic is a bad prime. We try to see how much of the theory of Dynkin-Kostant extends to this case. We also study the variety of Borel subgroups containing a unipotent element and prove a purity property for its cohomology in certain cases in bad characteristic.
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Character sheaves on disconnected groups, VII
We define and study convolution of parabolic character sheaves. As an application we attach to any parabolic character sheaf the orbit of a tame local system on the maximal torus under a subgroup of the Weyl group.
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Character sheaves on disconnected groups, VI
We define the notion of character sheaf on a possibly disconnected reductive group. We show that the restriction functor carries a character sheaf to a direct sum of character sheaves.
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Character sheaves on disconnected groups, V
We continue the study of character sheaves on a not necessarily connected reductive group. We prove orthogonality formulas for certain characteristic functions.
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Character sheaves on disconnected groups, IV
Let G be a possibly disconnected reductive group over a finite field with Frobenius map F. The main result of this paper is that the characteristic functions af "admissible complexes" A on G such that F^*A is isomorphic to A form a basis of the space of functions on G^F that are constant on G^{0F}-conjugacy classes.
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A q-analogue of an identity of N. Wallach
N.Wallach has considered an element of the group algebra of the symmetric group S_n which is the sum of an n-cycle, an (n-1)-cycle,...,a 2-cycle and the identity. He showed that multiplication by this element has eigenvalues 0,1,2,...,n-2,n. We prove a q-analogue of this result in which the group algebra of S_n is replaced by the corresponding Hecke algebra.
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Convolution of almost characters
In this paper we show that the convolution product of "almost characters" of a connected reductive group over a finite field is given by "structure constants" whose leading coefficients can be interpreted in K-theoretic terms and in particular are natural numbers.
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Character sheaves and generalizations
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
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Character sheaves on disconnected groups, III
We continue the attempt to develop a theory of character sheaves on a not necessarily connected reductive algebraic group. In this paper we introduce and study the generalized Green functions.
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Character sheaves on disconnected groups, II
The main theme of this paper is establishing the "generalized Springer correspondence" in complete generality that is, for not necessarily connected reductive algebraic groups.
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Character sheaves on disconnected groups, I
We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.
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Parabolic character sheaves, II
The theory of character sheaves on a reductive group is extended to a class of varieties which includes the strata of the De Concini-Procesi completion of an adjoint group.
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Parabolic character sheaves, I
We study a class of perverse sheaves on the variety of pairs (P,gU_P) where P runs through a conjugacy class of parabolics in a connected reductive group G and gU_P runs through G/U_P. This is a generalization of the theory of character sheaves.
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Representations of reductive groups over finite rings
We discuss a cohomological construction of representations of a reductive group over the ring of power series over a finite field modulo the r-th power of the maximal ideal. The case r=1 goes back to Deligne and the author. The case where r is greater than 1 was given without proof in the author's work in 1977. Here we supply the proofs and give some further results.
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Homomorphisms of the alternating group A_5 into a reductive group
We show that any two homomorphisms of the alternating group A_5 into E_8 (over the complex numbers) whose images has finite centralizers are conjugate under E_8. This, in conjunction with earlier work of Frey, completes the classification up to G-conjugacy of homomorphisms of A_5 into a simple adjoint algebraic group over the complex numbers.
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Classification of unipotent representations of simple p-adic groups,II
Let G(K) be the group of K-rational points of a connected adjoint simple algebraic group defined over a non-archimedean local field K. In this paper we classify the unipotent representations of G(K) in terms of the geometry of the Langlands dual group. (This was known earlier in the special case where G(K) is an inner form of a split group.) We also determine which representations are tempered or square integrable.
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